To solve this problem, we need to calculate the mean, median, mode, and range of the given dataset and match them to the corresponding values in the provided table.
Here is the dataset:
[tex]\[ 200, 100, 170, 180, 130, 130, 170, 130, 180, 100, 190, 110, 160, 210, 240 \][/tex]
### Calculations:
1. Mean:
The mean (average) is the sum of all values divided by the number of values.
[tex]\[
\text{Mean} = \frac{200 + 100 + 170 + 180 + 130 + 130 + 170 + 130 + 180 + 100 + 190 + 110 + 160 + 210 + 240}{15} = 160.0
\][/tex]
2. Median:
The median is the middle value when the data is ordered from least to greatest.
[tex]\[
\text{Ordered data} = [100, 100, 110, 130, 130, 130, 160, 170, 170, 180, 180, 190, 200, 210, 240]
\][/tex]
Since there are 15 values, the median is the 8th value in the ordered list:
[tex]\[
\text{Median} = 170
\][/tex]
3. Mode:
The mode is the most frequently occurring value in the dataset.
[tex]\[
\text{Mode} = 130
\][/tex]
4. Range:
The range is the difference between the maximum and minimum values.
[tex]\[
\text{Range} = 240 - 100 = 140
\][/tex]
### Matching to the table:
- Mean: 160 → (C)
- Median: 170 → (G)
- Mode: 130 → (I)
- Range: 140 → (P)
Therefore, the correctly matched values are:
\begin{tabular}{|l|c|c|c|c|}
\cline { 2 - 5 } \multicolumn{1}{c|}{} & 130 & 140 & 160 & 170 \\
\hline Mean & & & (C) & \\
\hline Median & & & & (G) \\
\hline Mode & (I) & & & \\
\hline Range & & & & (P) \\
\hline
\end{tabular}
